The Impact of Tortuosity on Chloride Ion Diffusion in Slag ......The Impact of Tortuosity on Chloride Ion Diffusion in Slag-Blended Cementitious Materials AkiraHatanaka,Yogarajah Elakneswaran

The Impact of Tortuosity on Chloride Ion Diffusion in Slag-Blended Cementitious MaterialsAkira Hatanaka, Yogarajah Elakneswaran Kiyofumi Kurumisa, , Toyoharu NawaJournal of Advanced Concrete Technology, volume ( ), pp.15 2017 426-439

Multi-scale Modeling of Concrete Performance- Integrated Material and Structural MechanicsKoichi Maekawa , Tetsuya Ishida Toshiharu Kishi,Journal of Advanced Concrete Technology, volume ( ), pp.1 2003 91-126

Effect of the key mixture parameters on tortuosity and permeability of concreteShamsad Ahmed, Abul Kalam Azad Kevin F. Loughlin,Journal of Advanced Concrete Technology, volume ( ), pp.10 2012 86-94

Enhanced model and simulation of hydration process of blast furnace slag in blended cementYao Luan , Tetsuya Ishida Toyoharu Nawa, , Takahiro SagawaJournal of Advanced Concrete Technology, volume ( ), pp.10 2012 1-13

https://www.jstage.jst.go.jp/article/jact/1/2/1_2_91/_pdfhttps://www.jstage.jst.go.jp/article/jact/10/3/10_3_86/_pdfhttps://www.jstage.jst.go.jp/article/jact/10/1/10_1_1/_pdfhttp://www.editorialmanager.com/jact/default.aspxhttp://www.j-act.org/index.html

Journal of Advanced Concrete Technology Vol. 15, 426-439, August 2017 / Copyright © 2017 Japan Concrete Institute 426

Scientific paper

The Impact of Tortuosity on Chloride Ion Diffusion in Slag-Blended Cementitious Materials Akira Hatanaka1, Yogarajah Elakneswaran2*, Kiyofumi Kurumisawa3 and Toyoharu Nawa4

Received 26 December 2016, accepted 19 August 2017 doi:10.3151/jact.15.426

Abstract The purpose of this study is to determine the tortuosity of cementitious materials containing blast furnace slag (BFS). Furthermore, the influence of tortuosity on multi-species transport into these materials is studied. The porosity and dif-fusivity of calcium silicate hydrate (C-S-H) were predicted using a three-dimensional spatial distribution model, which were then fitted to Archie’s law to determine tortuosity. The tortuosity increased with the slag replacement ratio, sug-gesting that the diffusion path for ions becomes complicated and lengthy due to slag addition. Thermoporometry was used to determine the pore size distribution of hydrated slag-blended cement. A partial replacement of ordinary Portland cement (OPC) with BFS modified the mineralogy (especially in the types of C-S-H), resulting in changes to the pore structure. The determined tortuosity and porosity were used in a reactive transport model to predict multi-species trans-port. Experimentally measured and simulated chloride profiles were in good agreement for hydrated OPC and slag-blended cements exposed to sodium chloride solutions. The causes for the low penetration rate of chloride in slag-blended cementitious materials are discussed considering their pore structure and surface electrical properties. The role of tortuosity on Cl-/OH- for the evaluation of chloride induced corrosion was also discussed.

1. Introduction

Cementitious materials are used in low and intermediate radioactive waste disposal facilities (Hostics and Gens 2016). Increased amounts of blended cement consisting blast furnace slag (BFS) or fly ash are expected to see use in such facilities going forward, due to their lower diffusivity and high chemical resistance compared to conventional ordinary Portland cement (OPC) (Niwase et al. 2010). Therefore, it has been considered that the use of cementitious materials blended with BFS is an effective method to improve their durability. The dura-bility performance of cementitious materials in service environments is affected by numerous factors, many of which involve attacks due to ionic transport, leading to reduced service life. The durability of cementitious ma-terials must be ensured in both an economically and environmentally responsible manner. In reinforced con-

crete structures, corrosion of the reinforcing steel is the cause of the most serious durability problems (Malhorta 2000). Extreme environments prompt the ingress of aggressive ions into the concrete and lead to degradation of the concrete structure over time. Accurate estimation of the time it takes for chloride ions to reach the rein-forcement is a crucial parameter for estimating the ser-vice life of reinforced concrete structures. Chloride penetrates the concrete via adsorption on its surface and further transports to greater depths into the concrete by diffusion (Yu and Page 1991). A number of factors such as porosity, tortuosity, type and amount of hydrates, and characteristics of calcium silicate hydrate (C-S-H) con-tribute to the concentration of free chloride in the pore solution of concrete for initiating and promoting the corrosion process; these factors have been extensively studied using several different experimental techniques and modeling approaches (Samson and Marchand 2007; Johannesson et al. 2007; Hosokawa et al. 2011; Glasser et al. 2008).

Tortuosity is an important factor for understanding and predicting the diffusion of chloride ions into cemen-titious materials. It is related to effective diffusivity through either geometric tortuosity or apparent tortuos-ity which considers both geometric tortuosity and con-strictivity, and tortuosity depends on the material mor-phology (Patel et al. 2016). Archie’s law has been used previously to fit the tortuosity of cementitious materials, with fitted values of 0.94–4.8 (Yamaguchi et al. 2009). Further, Jennings reported a fractal dimension value of 2.73 for the tortuosity (Jennings 2000). A review of the literature shows that it is difficult to directly determine tortuosity in an experimental manner (Ando et al. 2015; Kikuchi et al. 2009; Nakarai et al. 2006; Promentilla et

1Graduate student, Division of Sustainable Resources Engineering, Faculty of Engineering, Hokkaido University, Sapporo, Japan. 2Specially Appointed Associate Professor, Division of Sustainable Resources Engineering, Faculty of Engineering, Hokkaido University, Sapporo, Japan. *Corresponding author, E-mail: [email protected] 3Associate Professor, Division of Sustainable Resources Engineering, Faculty of Engineering, Hokkaido University, Sapporo, Japan. 4Professor, Division of Sustainable Resources Engineering, Faculty of Engineering, Hokkaido University, Sapporo, Japan.

A. Hatanaka, Y. Elakneswaran*, K. Kurumisawa and T. Nawa / Journal of Advanced Concrete Technology Vol. 15, 426-439, 2017 427

al. 2009). Different researchers have reported different values for tortuosity obtained using various analytical methods, and hence an appropriate method that consid-ers its physical definition merits the development.

This study proposes a method to determine the tortu-osity of hydrated OPC and slag-blended cement from the porosity and diffusivity of C-S-H, predicted by a three-dimensional spatial distribution model proposed previously (Kurumisawa et al. 2012). Furthermore, a relationship between the slag replacement ratio and tor-tuosity was derived. The determined tortuosity values were incorporated into the reactive transport model de-veloped previously (Elakneswaran et al. 2010) to pre-dict chloride transport slag-blended cementitious mate-rials. Thermodynamic equilibrium reactions between hydrates and solution, binding of chloride on hydrates (both C-S-H and monosulfate), and the influence of surface charge on multi-species transport were also con-sidered in the reactive transport model in addition to porosity, pore size and tortuosity effects. Finally, the impact of tortuosity on the ratio of chloride to hydroxyl concentration for evaluating the long-term reinforce-ment corrosion was discussed.

2. Experimental

2.1 Materials and sample preparation The chemical compositions and physical properties of OPC and BFS are given in Table 1. Hydrated cement paste (HCP) was prepared with water to binder ratios (W/B) of 0.3, 0.5, and 0.7, and BFS cement paste (BFSCP) was prepared with a water to binder ratio of 0.5 with BFS replacement ratios of 50% and 70%. Sam-ples were cast in molds (φ50 mm × 100 mm or 40 mm × 40 mm × 160 mm) after mixing and continuous hand-mixing every 30 min to stop bleeding. Samples were sealed for 24 h at room temperature, and then cured in water for 28 or 91 days at 20 °C. 2.2 Backscattered electron image (BEI) and En-ergy Dispersive X-ray spectrometry (EDX) measurements Cubes 5 mm in length per side were cut from freeze-dried material after curing, for use in BEI and EDX measurements. Specimens were immersed in epoxy resin under vacuum, and after hardening the resin the specimen surfaces were polished using SiC paper. Pol-ished surfaces were smoothed using 0.25 μm diamond paste, and a Pt layer was applied to provide electric conductivity on the surface. Electron microscopy imag-ing was conducted under the following conditions: an acceleration voltage of 15 keV, working distance of 17

mm, area size of 200 × 150 μm, and pixel size of 0.32 μm. The resulting resolution in this study was 0.32 μm, and as such pores smaller than 0.32 μm in diameter could not be distinguished. Observations were carried out on 20 areas in each specimen. Unhydrated cement (UH), unhydrated BFS, calcium hydroxide (CH), C-S-H including other hydrates, and pores larger than 0.32 μm in diameter were distinguished using image analysis software and setting brightness thresholds. The average fraction of each phase was considered to be the volume fraction (Igarashi et al. 2004). The measured CaO/SiO2 (C/S) and Al2O3/SiO2 (A/S) ratios of C-S-H are the average of 20 EDX measurements on each specimen. The C/S and A/S were corrected by standard materials (Wollastonite and Jadeite). 2.3 Electron probe microanalyzer (EPMA) measurements After curing, the cylinder samples were cut into two halves and all surfaces except the cutting face were coated with epoxy resin to ensure chloride penetration in only one direction. The coated samples were exposed to 0.5 mol/l chloride for 28 or 91 days. After exposure, the specimens were cut into two halves parallel to the path of ionic ingress; one part was used for EPMA map-ping while the other was used to determine the amount of chloride by a traditional method. An EPMA JEOL JXA-8900M apparatus was used to carry out element mapping. The measurement conditions were as follows: 15 kV accelerating voltage, 50 mA beam current, 60 × 30 μm pixel size, and 1000 × 50 points. The chloride profile was calculated from the mapping, but was ex-pressed as X-ray counts of chloride. The counts were corrected by the determining the chloride concentration from a wet analysis as described in Japanese Industrial Standard (JIS) A 1154. In the wet analysis, powder sam-ples were mixed with 2 M nitric acid solution and boiled for 5 min. The boiled solution was filtered and the con-centration of chloride in the solution was measured with ion chromatography. 2.4 Micro-elastic modulus measurements using micro-indentation method The same specimens which were used for BEI were used here. The elastic moduli of the hydration products were measured using a Fischers scope (HC-100), and 100 indents in a 10 × 10 μm grid were measured in each specimen. The maximum load and speed of the applied load were 20 mN and 1 mN/s respectively. The average value of the measurements in each specimen was deter-mined as the micro elastic modulus of C-S-H.

Table 1 Chemical composition and physical properties of raw materials. Chemical composition (%) Density (g/cm3)

Blaine (cm2/g) SiO2 Al2O3 Fe2O3 CaO MgO TiO2 Na2O K2O SO3 Cl

OPC 3.16 3310 21.56 4.68 2.98 65.63 1.3 0.23 0.33 0.33 1.9 0.005BFS4000 2.91 3930 34.03 14.36 0.83 43.28 6.51 0.46 0.18 0.31


2.5 Pore size distribution by thermoporometry Differential scanning calorimetry (DSC) was used to measure the pore size distributions of hydrated samples. For each sample, approximately 28 mg of material was dried at 105 °C for 24 h and immersed in water for 3 h. After immersion, water adhered on the sample surface was wiped off and the samples were placed in an alumi-num sample pan. Alumina powder was used as a refer-ence specimen during measurement. The measurement range was 10 °C to -60 °C, and the scanning speed was 2 °C/min. The total moisture content was determined by the weight differences between measurements at 20 and 105 °C. Pore size distribution was determined using a thermoporometry theory reported previously (Brun et al. 1977). 2.6 Electric conductivity Specimen dimensions for electrical conductivity meas-urements were 40 × 40 × 40 mm. Stainless electrodes (40 × 30 × 0.3 mm) were placed on the specimen 30 mm apart, and the effective area of the electrode was 30 × 30 mm. AC impedance of the specimens was meas-ured over a frequency range of 4 Hz to 5 MHz with an impedance analyzer (HIOKI IM3570) at an applied voltage of 0.1 V. Nyquist plots were established using the measured data, and the bulk resistivity was deter-mined from the point where the electrode resistivity (straight line) and the circle is intersected (Kurumisawa et al. 2012), using

aR LA

ρ = (1)

1σρ

= (2)

where ρ is the bulk resistivity of the specimen, Ra is the measured resistance, L is the distance between elec-trodes, A is the effective area of the electrode, and σ is the conductivity. The measured electrical conductivity is the normalized conductivity in which the influence of the pore solution is removed by dividing the measured electric conductivity by the pore solution conductivity. The pore solution conductivity was calculated based on hydration degree and the chemical composition of ce-ment (Snyder et al. 2003). 3. Modeling approach

3.1 Reactive transport model An integrated thermodynamic model considering ion–ion and ion–solid interactions was used to simulate multi-ionic transport. The model was implemented in the PHREEQC geochemical code using phase-equilibrium, surface complexation, and multi-component diffusion (MCD) modules. Thermodynamic properties for various phases and minerals present in the cement system were collected from CEMDATA07 (Lothenbach et al. 2008) and other sources (Myers et al.

2014), and converted into a format suitable for PHRE-EQC. The converted data, together with the PHREEQC default thermodynamic database (Parkhust and Appelo 1999), were used in this study for each calculation. The details of the integrated thermodynamic model are de-scribed elsewhere (Elakneswaran et al. 2010).

The diffusive flux of a selected ion, i, considering concentration and electrical potential gradients and the chemical activity effects can be expressed by Nernst-Planck equation as follows (Elakneswaran et al. 2010):

,1

, , 2,1

ln( )1

ln( )ln( )1

ln( )

n jiw j jj

ji ii w i w i i i n

i w j j jj

cD z

c xcJ D D z c

c x D z c

γ

γ =

=

∂∂+

∂ ∂∂ ∂= − + +

∂ ∂

⎡ ⎤⎢ ⎥

⎡ ⎤ ⎣ ⎦⎢ ⎥⎣ ⎦

∑

∑ (3)

where Dw,i is its diffusion coefficient, γi is its activity coefficient, ci is its concentration, and zi is its valance; the subscript j is introduced to show that these species are for the potential term. The diffusion coefficient of ions in a porous medium, Dp, is related to Dw,i, porosity, ε, and tortuosity, τ, by Archie’s law (Appelo and Postma 2009):

,p w i wD Dτε= (4)

3.2 Three-dimensional spatial distribution model 3.2.1 Autocorrelation function calculations To reconstruct a three-dimensional spatial image of the hardened cement paste, the autocorrelation function (ACF) was used for different phases (UH, CH, pores, slag and other phases) to generate a binary image from BEI without the C–S–H phase, which was not included because it is the matrix and acts as a continuous phase in the hardened cement paste. The ACF is a two-point correlation function, defined as the probability that two arbitrary points are in the same phase as a function of the distance between them (Torquato 2001). Thus, the position of each phase can be determined using ACF. The following procedure was used for calculating ACF in this study (Bentz 2000). The summation of S(x,y) was determined for an M×N image using the following equation:

1 1

( , ) ( , )( , )( )( )

M x N y

i j

I i j I i x j yS x yM x N y

− −

= =

× + +=

− −∑ ∑ (5)

where I(x,y) is 1 if the pixel at location (x,y) contains the phase(s) of interest, and is 0 otherwise. S(x,y) is then converted into the S(r) function for the distance r be-tween pixels using bilinear interpolation of S(x,y) values as follows:

2

0

1( ) ( , )2 1 4

r

l

lS r S rr r

π=

=+ ∑ (6)


3.2.2 Three-dimensional spatial image recon-struction ACF S(r) was used to reconstruct a three-dimensional image of the microstructure for each phase. Pixels in the three-dimensional spatial image are assigned random numbers with a normal distribution of N(x, y, z), gener-ated using the Box–Muller method (Bentz and Garboczi 1991). This random number distribution of N(x, y, z) is modified using a filter function F(x, y, z) using the ACF S(r). Finally, the resultant image R(x, y, z) is generated using the following equation:

30 30 30

0 0 0( , , ) ( , , ) ( , , )

i j kR x y z N x i y j z k F i j k

= = == + + + ∗∑ ∑ ∑ (7)

where ( , , )F x y z is determined as

[ ]

2 2 2( ) (0) (0)( ) ( , , )

(0) (0) (0)

S r x y z S SF r F x y z

S S S

⎡ ⎤= + + − ×⎣ ⎦= =− ×

(8)

The threshold operation was carried out to obtain ap-propriate volume fractions in regards to the pixels in R(x, y, z), which were originally assigned to the respective phases of interest (UH, pores, BFS, or CH). For exam-ple, if a value of R(x, y, z) is larger than the critical threshold, the pixel is assigned to the phase of interest; otherwise, it is assigned to the original phase. The reas-signed number of pixels corresponds to measured vol-ume fraction using the BEI. The reconstructed size of the image is 1003 voxels where one voxel is equivalent to 0.32 μm3 according to the BEI observations. Three different images with different random numbers were reconstructed to confirm the reproducibility of the model; periodic conditions were also applied to all faces.

An outline of the 3D spatial reconstruction model is illustrated in Fig. 1. The area fraction of each phase was calculated from scanning electron microscopy (SEM) images, and 3D-spatial distribution models from the calculated area functions. Finally, the diffusivity of C-S-H was derived from this model as electrical conductivity. In this model, the input parameter is the diffusivity of C-S-H and the capillary pore, and the output parameter is diffusivity of a given specimen; this analysis is de-scribed further in section 4.3.

4. Results and discussion

4.1 CaO/SiO2, Al2O3/SiO2 ratios and BEI The CaO/SiO2 (C/S) and Al2O3/SiO2 (A/S) ratios of BFSCP are shown in Fig. 2 as functions of the slag re-placement ratio. The A/S ratio increases while the C/S ratio decreases with increasing BFS replacement ratio,

Deriving the correlat on betw een d iffusivity and porosity of C-S-H

Specim ens

Reconstruction 3-d im ensional sp atia ld istrib u tion m odel

Estim ate of the electric conductivity・ load 3D-spatia l d istribution m odel asan electrica l circu it m odel

INPUTD iffusivity of C-S-H

D iffusivity of Pore

OutputD iffusion coefficient of a

spec men（ unknow n value）

SEM image

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 10 20 30 40 50 60

S(r)

ｒ(ピクセル)

C‐H

UH

S

pore

r( p ixe l)

Derive au tocorrelationfunctions of every phases

空隙 CH C ‐S‐H

UH スラグ

Pore

Slag

As an electriccircuit model ・・・

Constructing 3D-spatiald istribution model from

autocorrelationfunctions

Electricalconductivity

Same value

Pore

C-S-H

Others

Fig. 1 Procedures for deriving the relationship between the diffusivity and porosity of C-S-H.

0.000.020.040.060.080.100.120.140.160.180.20

0.00.20.40.60.81.01.21.41.61.82.0

0 20 40 60 80

Al 2O3/SiO2

CaO

/SiO

2

Slag substitution（％）

C/S

A/S

Fig. 2 CaO/SiO2 and Al2O3/SiO2 ratios as functions of slag replacement ratio.


which is consistent with previous reports (Taylor et al. 2010). Some of the silica in C-S-H is substituted by aluminum to form C-A-S-H in slag-blended cement. The A/S ratio also increases as Al2O3 increases with slag addition. The experimental results show the presence of aluminum in the C-S-H of HCP as reported in previous studies (Lothenbach et al. 2011; Kocaba 2009). These ratios modify the structure of C-S-H/C-A-S-H and can affect the durability performance of concrete. BEIs of HCP and BFSCP of 50% and 70% replacement after 91 days of curing are shown in Fig. 3. Unreacted BFS is

still present in the sample after 91 days of curing. In this study, BEIs were separated into five phases based on brightness: pores are black, calcium hydroxide is dark gray, C-S-H is light gray, unhydrated cement is white and unreacted BFS is bright white. The area fraction of each phase as determined by BEI experiments is shown in Fig. 4. As the hydration progress, the amount of hy-dration products increase, and the pore and un-hydrated cement and slag decrease. The increase of calcium hy-droxide in BFSCP with hydration time is observed in the figure. This might be due to different in the hydra-

75μm

CH

Pore

C-S-H

75μm

75μm

Slag

UH

Fig. 3 Backscattered electron images of HCP (left), and BFSCPs of 50% (center) and 70% replacement (right).

0

10

20

30

40

50

60

70

80

90

100

o50 o70 b50 b70

Area fraction

(%)

Curing period: 28 days

Slag

Pore

CH

CSH

UH

0

10

20

30

40

50

60

70

80

90

100

o50 o70 b50 b70

Area fraction

(%)


Slag

Pore

CH

CSH

UH

Fig. 4 Area fractions determined by BEI experiments. Notation: o50: OPC-W/B (%); b50: BFS-percentage of slag re-placement (W/B=0.5).


tion degree; hydration of cement is higher than that of slag in this study. The amount of calcium hydroxide will not affect the other calculation results because C-S-H dominates the volume of hydration products. Three-dimensional spatial image models were reconstructed based on an autocorrelation function (described in sec-tion 3.2) derived from these backscattered electron im-ages. 4.2 Electrical conductivity The results of electrical conductivity measurements of HCP and BFSCP are shown in Fig. 5. The electric con-ductivity of each specimen decreases with increasing BFS replacement ratio for each W/B, and decreases with decreasing W/B. The electrical conductivity of cementi-tious materials generally depends on porosity, pore con-nectivity and pore solution conductivity. The influence of W/B on the electrical conductivity is linked to changes in porosity: decreasing W/B decreases the po-rosity and thus lowers the electrical conductivity due to limited paths for ionic movement. The electrical con-ductivity of the pore solution becomes significant when the specimens have the same porosity. Pore solution concentration (especially in regards to sodium and po-

tassium ions) decrease with BFS replacement ratio, re-ducing the conductivity. 4.3 Determination of tortuosity from diffusivity and porosity of C-S-H The porosity of C-S-H can be determined by the rela-tionship between its elastic modulus and porosity (Jennings et al. 2007),

0.5 0.0077C S H microEϕ − − = − × (9)

where C S Hϕ − − is the porosity of C-S-H and microE is the elastic modulus of C-S-H. The median value of the elas-tic modulus of hydrated cement and slag specimens, determined by a micro-indentation method, is consid-ered as the elastic modulus of C-S-H because it is the major phase (> 70% in volume). The results of the elas-tic modulus and calculated porosity of C-S-H are shown in Fig. 6.

The reconstructed three-dimensional spatial images were used to calculate the diffusion coefficient of HCP and BFSCP based on the model proposed by Garboczi and Bohn (2003). The diffusivity in a steady state condi-tion, as with conductivity, can be predicted by express-

0

0.05

0.1

0.15

0.2

0.25

0.3

0% 50% 70%

Electric Con

ductivity(S/m)

Slag substitution(%)

W/B=0.7

W/B=0.5

W/B=0.3

Fig. 5 Electric conductivity of HCP and BFSCP cured for 28 days.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

5

10

15

20

25

30

Porosity of C

‐S‐H

Elastic mod

ulus(GPa)

Elastic modulus

Porosity

Fig. 6 Elastic modulus and porosity of C-S-H. Notation: dx-y-z: curing period-W/B-slag replacement ratio.


ing it in the following Nernst-Einstein relation:

0 0

DD

σσ

= (10)

where D is the measured diffusivity, 0D is the diffusiv-ity of the ions in free water, σ is then measured electrical conductivity and 0σ is the conductivity of the pore so-lution.

In this model, the diffusivity of the capillary pore and C-S-H are necessary for estimating the diffusivity of the overall material. The diffusion coefficient of chloride ions in the capillary pores was held at 1.81×10-9 (m2/s) (Jensen et al. 1999). The diffusion coefficient of the C-S-H, the unknown parameter, was calculated based on the electric conductivity results given in Fig. 5. The relationship between the diffusion coefficient and poros-ity of C-S-H is shown in Fig. 7. In addition to the specimens considered in Fig. 6, HCP specimens pre-pared at W/B of 0.3 and 0.7 cured for 28 and 91 days and BFSCP specimens prepared at W/B of 0.4 and cured for 28 days were considered to determine diffusivity of C-S-H.

As shown in Fig. 7, the diffusion coefficient of C-S-H decreases with the slag replacement ratio in accordance with reported studies (Kurumisawa et al. 2012). The

relationship between the diffusion coefficient and the porosity of C-S-H can be fitted to Archie’s law (Eq. (4)) as follows for each slag replacement ratio to determine the tortuosity:

BFS replacement ratio of 0%： 9 2.38921.0 1.0C S HD ϕ−

− − = × ⋅ (11)

BFS replacement ratio of 50%： 9 2.63141.0 1.0C S HD ϕ−

− − = × ⋅ (12)

BFS replacement ratio of 70%： 9 2.84571.0 1.0C S HD ϕ

−− − = × ⋅ (13)

where C S HD − − is the diffusion coefficient of C-S-H and ϕ is the porosity of C-S-H. A value of 1.0×10–9 (m2/s) was assumed for the diffusion coefficient of ions in free water for best fit, considering the multi-species in the pore solution of hydrated cement and slag which typi-cally has a self-diffusion coefficient of 0.6 to 1.81×10–9 (m2/s). The determined tortuosity can be related to slag replacement ratio, rsg, as:

0.63 2.37sgrτ = + (14)

This relationship is plotted in Fig. 8. The increase in

y =10‐9x2.3892

R² = 0.9114

y = 10‐9 x2.6314

R² = 0.6329y = 10‐9 x2.8457

R² = 0.8727

0

2

4

6

8

10

12

14

16

18

0.2 0.25 0.3 0.35 0.4 0.45 0.5

Diffusivity of C‐S‐H (m

2 /s)

(x 10‐11)

Porosity of C‐S‐H

Diffusion coefficient and porosity of C‐S‐H

0%

50%

70%

Fig. 7 Relationship between diffusion coefficient and porosity of C-S-H.

y = 0.6265x + 2.3714R² = 0.9922

2.3

2.4

2.5

2.6

2.7

2.8

2.9

0 10 20 30 40 50 60 70 80

Tortuo

sity(τ)

Slag replacement ratio(%) Fig. 8 Relationship between tortuosity and slag replacement ratio.


tortuosity with slag replacement ratio indicates that the diffusion path of chloride ions becomes more complex as more slag is added. The estimated tortuosity values agree reasonably well with values reported in previous studies (Jennings 2000).

4.4 Pore structure The pore size distributions of HCP and BFSCP as de-termined by thermoporometry (28 and 91 days curing) are shown in Fig. 9. As assumed in a previous study (Jennings 2008), pores are classified as one of two types: small gel pores (< 5 nm) and large gel pores (5–10 nm). The number of small gel pores increases with the BFS replacement ratio, and the amount of large gel pores increases as the water to powder ratio increases. This is related to the pores in the different C-S-H phases: low-density C-S-H (LD C-S-H) and high-density C-S-H (HD C-S-H) (Tennis and Jennings 2000). LD C-S-H consists of large gel pores while HD C-S-H has small gel pores. Therefore, a large amount of LD C-S-H is formed at high W/B, and slag addition leads to the formation of HD C-S-H. Overall, the number of pores decreases and they become smaller with curing period increases. The characteristics of HD C-S-H and LD C-S-H are respectively similar to that of the inner- and outer-products of hydrating cement and/or slag due

to their porosity (Maekawa et al. 2003). Their micro-structure and properties can influence ionic diffusion through cementitious materials. The measured total po-rosity is used in the prediction of chloride ions diffusion. 4.5 Comparison between measured and esti-mated chloride ingress One-dimensional numerical analysis was performed to simulate cylindrical samples of HCP and BFSCP (50 mm diameter, 50 mm height) exposed to 1 L of 0.5 M NaCl solution for 28 and 91 days. Multi-species trans-port was performed considering common ions such as Na+, Cl-, K+, SO42-, Ca2+, Al3+, Si4+ and OH-. Self-diffusion coefficients of ions in free water for a speci-fied temperature were used as diffusion coefficients. In the simulations, the initial and final boundary conditions were set to 0.5 M NaCl and zero flux, respectively. The pore solution concentration and the amount of hydrates required for the simulations were calculated based on a hydration model reported previously (Elakneswaran et al. 2016). Although capillary pores are included in the diffusion path of chloride ions, it is considered that chloride diffusion is controlled by C-S-H because the amount of C-S-H is more than 70% in volume of speci-men from the result of BEI as shown in Fig. 4. The chloride ions diffuse through a series of pores having

0

100

200

300

400

500

600

700

800

900

1 10 100

dv/dLogr(m

g/g)

Pore radius（nm）

0.5‐00.5‐500.5‐700.7‐0


0

100

200

300

400

500

600

700

800

900

1000

1 10 100

dv/dLogr(m

g/g)

Pore radius（nm）

0.5‐0

0.5‐50

0.5‐70

0.7‐0


Fig. 9 Pore size distribution of HCP and BFSCP. Notation: W/B-slag replacement ratio.


various diameter. A cylindrical pore shape having a sin-gle size was assumed for the diffusion, which plays a critical influence on the ionic diffusion. The size of the critical pore was assumed based on the pore size distri-bution and the surface areas of C-S-H. The pore consists of free water and diffuse double layer, and the volume of free water is used to calculate surface area. The other necessary input parameters such as porosity (from ther-moporometry measurements), tortuosity (calculated in section 4.3), and assumed pore radius are tabulated in Table 2.

Figure 10 compares the calculated and experimental total chloride profiles. The predicted amounts of chloride in the free water of the pore solution, diffuse double layer, chemically bound as Friedel’s salt, and adsorbed

on C-S-H surface are also presented. Although several different mechanisms are present, the physical adsorp-tion of chloride dominates total, which supports previ-ous experimental studies in blended cements (Saeki and Sasaki 2006). The presence of AFm phases, which is more pronounced in slag-blended cements than conven-tional Portland cements, contributes to the chemical binding of chloride. BFSCP shows lower penetration rates than those of HCP over both exposure periods due to changes to the mineralogy and pore structure as more slag is added. Furthermore, high addition of slag leads to better resistance for chloride transport.

The calculated tortuosity suggests that the diffusion path of BFSCP is longer than that of HCP. Hydration of cement and slag, and the associated microstructure de-velopment mechanisms proposed by Maekawa and as-sociates (Maekawa et al. 2003; Luan et al. 2012), were considered here to propose a chloride diffusion path (Fig. 11). Ionic diffusion occurs in the pores of both the inner and outer products, and threshold pores or bottle-neck exists in the inner products. The pores in the inner products are very small in size, and would be com-pletely covered by the electrical double layer (EDL). 5 nm radius pores are fully filled EDL in HCP (Elaknes-waran et al. 2010), but this size dimension is larger in BFSCP because of the lower ionic strength of the pore solution compared to HCP. Ionic diffusion through the pores of outer products has less effect from surface charge of C-S-H, but the diffusion is greatly affected by

Table 2 Porosity, tortuosity, and pore radius used in simulations.


W/B-slag replacement ratio Porosity Tortuosity Pore radius(nm) 0.5-0 0.245 2.39 3.2 0.5-50 0.253 2.63 2.3 0.5-70 0.259 2.85 2.1 0.7-0 0.332 2.39 3.4

Curing period: 91 days 0.5-0 0.200 2.39 3.2 0.5-50 0.214 2.63 2.3 0.5-70 0.226 2.85 2.1 0.7-0 0.311 2.39 3.4

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of Cl‐ (mg/g)

Distance(mm)

d28‐0.5‐0

Exp.TotalBulk waterDDLChemicalPhysical

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of C

l‐ (mg/g)

Distance(mm)

d28‐0.5‐50

Exp.

Total

Bulk water

DDL

Chemical

Physical


0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of Cl‐ (mg/g)

Distance(mm)

d28‐0.7‐0


0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of Cl‐ (mg/g)

Distance(mm)

d28‐0.5‐70


0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of Cl‐ (mg/g)

Distance(mm)

d91‐0.5‐0


0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of Cl‐ (mg/g)

Distance(mm)

d91‐0.5‐50



surface charge in the pore of inner products. When the pores of the outer and inner products are connected (Fig. 11), diffusion through the inner products controls the overall diffusion rate. This is significant in slag-blended cement due to having large EDL thickness, high tortuos-ity, and small threshold pore size, which change with the slag replacement ratio to promote a lower penetration rate.

4.6 Simulation results on evaluation of rein-forcement corrosion The Cl-/OH- ratio is a useful parameter for evaluating reinforcement corrosion in concrete structures. For Cl-/OH- ratio, Cl- is the summation of the total chloride concentration in free solution and in the diffuse double layer, and OH- was calculated based on the pore solution pH. The threshold value of Cl-/OH- to initiate corrosion is 3–5 (Kari et al. 2013). The impact of slag addition on the ratio at a depth of 45 mm as a function of exposure

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of Cl‐ (mg/g)

Distance(mm)

d91‐0.5‐70


0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Conten

t of Cl‐ (mg/g)

Distance(mm)

d91‐0.7‐0


Fig. 10 Comparison between measured and simulated chloride profiles for HCP and BFSCP after 28 and 91 days of 0.5 M NaCl exposure. Notation: dx-y-z: curing period-W/B-slag replacement ratio; Exp.: Experimentally measured total Cl-; Total: Predicted total Cl-; Bulk water: Predicted free Cl- in bulk pore water; DDL: Predicted free Cl- in diffuse double layer; Chemical: Predicted chemically bound Cl-; Physical: Predicted physically adsorbed Cl- on C-S-H.

Outer products

Inner products

Coreparticle

Distance x

Poro

sityφ

０

φin

φout

Capillarypore

C-S-Hgrains

Critica l- rad iu s

Ou ter

p rodu ctsOu ter

p rodu cts

In n er

p rodu cts

bottleneck

Fig. 11 Concept of ionic diffusion path considering tortuosity and bottleneck pores.


period is presented in Fig. 12. Input parameters for the simulations are the same as described in section 4.5. Slag-blended cement shows better performance against chloride-induced corrosion than Portland cement. Cor-rosion initiation for a Cl-/OH- ratio of 3.0 in slag-blended cement is 10 years longer than that of OPC, and the reinforcement in OPC starts to corrode after 30 years for a threshold ratio of 5.0; slag-blended cement serves more than 100 years under similar conditions. Another simulation was performed to evaluate the im-pact of tortuosity on the Cl-/OH- ratio. The simulation results of Cl-/OH- ratio at a depth of 45 mm for OPC are shown in Fig. 13. Higher tortuosity leads to a low Cl-/OH- ratio and longer service life of the concrete against chloride attack as a result. This is remarkable for a tor-tuosity value of 3.5. The simulation results show that a partial substitution of OPC by slag, in combination with increasing tortuosity, are important factors to reduce Cl-/OH- ratio as pertains to chloride induced corrosion. As such, these factors should be considered in the material design of concrete structures exposed to chloride-rich environments.

5. Conclusions

The tortuosity of hydrated cementitious materials blended with slag was determined by fitting the porosity and diffusivity of C-S-H, predicted through a three-

dimensional spatial distribution model, to Archie’s law. The determined tortuosity is linearly related to the slag replacement ratio which indicates that ionic diffusion path becomes longer after a partial replacement of OPC with slag. Hydration of cement and slag forms LD C-S-H and HD C-S-H, and the associated pores are small gel pores (< 5 nm) in HD C-S-H and large gel pores in LD C-S-H. The amount of the small and large pores de-pends on W/B, slag addition, and curing period; large gel pores form at high W/B, and slag addition creates more small gel pores. The chloride profiles predicted using the determined tortuosity and porosity agree well with the measured profiles for both HCP and BFSCP exposed to 0.5 M NaCl solution for 28 and 91 days, predicted physical adsorption of chloride controls the total. The addition of slag leads to large EDL thickness, high tortuosity, and small threshold pore size which shows high chloride penetration resistance in slag-blended cementitious materials. The simulation results on Cl-/OH-, an indicator for evaluating the chloride in-duced corrosion, show that high durability of reinforced concrete can be achieved with slag addition and in-creased tortuosity values. Acknowledgements This study was financially supported by JSPS KA-KENHI Grant No:16K1812906 and 16K0656306. A part of this study was conducted at the Joint-use Facili-

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60 70 80 90 100

[Cl‐ ]/[OH‐ ][‐]

Time [year]

OPC

Slag

Fig. 12 Cl-/OH- ratio at a depth of 45 mm as a function of exposure time for hydrated OPC and slag-blended cement ex-posed to 0.5 M NaCl.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60 70 80 90 100

[Cl‐ ]/[OH‐ ][‐]

Time [year]

2.5

3.0

3.5

Fig.13 Cl-/OH- ratio at a depth of 45 mm as a function of exposure time for hydrated OPC with different tortuosity values exposed to 0.5 M NaCl.


ties: Laboratory of Nano-Micro Material Analysis at Hokkaido University, supported by the Nanotechnology Platform Program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. References Ando, M., Kobayashi, H., Uenaka, S. and Nawa, T.,

(2015). “Quantification of tortuosity of pore network for diffusion of chloride ion transport into hardened cement paste.” Cement Science and Concrete Technology, 69, 96-103. (in Japanese)

Appelo, C. A. J. and Postma, D., (2009). “Geochemistry, groundwater and pollution.” CRC Press Taylor & Francis Group.

Bentz, D. P., (2000) “CEMHYD3D: A three-dimensional cement hydration and microstructure development modelling package version 2.0.” NISTIR 648

Bentz, D. P. and Garboczi, E. J., (1991). “Percolation of phases in a three-dimensional cement paste microstructural model.” Cement and Concrete Research, 21(2-3), 325-344.

Bohn, R. B. and Garboczi, E. J., (2003). “User Manual for Finite Element and Finite Difference Programs: A Parallel Version of NIST IR 6269.”

Brun, M., Lallemand, A., Quinson, J. F. and Eyraud, C., (1977). “A new method for the simultaneous determination of the size and shape of pores: The thermoporometry.” Thermochimica Acta, 21(1), 59-88.

Elakneswaran, Y., Iwasa, A., Nawa, T. and Kurumisawa, K., (2010). “Ion-cement hydrates interactions govern multi-ionic transport model for cementitious materials.” Cement and Concrete Research, 40, 1756-1765.

Elakneswaran, Y., Owaki, E., Miyahara, S., Ogino, M., Maruya, T. and Nawa, T., (2016). “Hydration study of slag-blended cement based on thermodynamic considerations.” Construction and Building Materials, 124, 615-625.

Glasser, F. P., Marchand, J. and Samson, E., (2008). “Durability of concrete - degradation phenomena involving detrimental chemical reactions.” Cement and Concrete Research, 38(2), 226-246.

Hosokawa, Y., Yamada, K., Johanneson, B. and Nilsson, L.-O., (2011). “Development of a multi-species mass transport model for concrete with account to thermodynamic phase equilibrium.” Materials and Structures, 44, 1577-1592.

Hostics, V. L. and Gens, R., (2016). “Performance assessment of concrete structures and engineered barriers for nuclear applications - Conclusions of RILEM TC226-CNM.” Springer Nature.

Igarashi, S., Kawamura, M. and Watanabe, A., (2004). “Analysis of cement pastes and mortars by a combination of backscatter-based SEM image analysis and calculations based on the Powers model.” Cement and Concrete Composites, 26(8),

977-985. Jennings, H. M., (2000). “Model for the microstructure

of calcium silicate hydrate in cement paste.” Cement and Concrete Research, 30(1), 101-116.

Jennings, H. M., (2008). “Refinements to colloid model of C-S-H in cement: CM-II.” Cement and Concrete Research, 38, 275-289.

Jennings, H. M., Thomas, J. J., Gevrenov, J., Constantinides, G. and Ulm, F.-J., (2007). “A multi-technique investigation of the nanoporosity of cement paste.” Cement and Concrete Research, 37(3), 329-336.

Jensen, O. M., Freiesleben Hansen, P., Coats, A. M. and Glasser, F. P., (1999). “Chloride ingress in cement paste and mortar.” Cement and Concrete Research, 29 (9), 1497-1504.

Johannesson, B., Yamada, K., Nilsson, L.-O. and Hosokawa, Y., (2007). “Multi-species ionic diffusion in concrete with account into interaction between ions in the pore solution and the cement hydrates.” Materials and Structures, 40(7), 651-665.

Kari, O. P., Elakneswaran, Y., Nawa, T. and Puttonen, J., (2013). “A model for a long-term diffusion of multispecies in concrete based on ion-cement-hydrate interaction.” Journal of Materials Science, 48(12), 4243-4249.

Kikuchi, M., Sasaki, K., Suda, Y. and Saeki, T., (2009). “Effect of chemical composition of C-S-H on chloride diffusion.” Cement Science and Concrete Technology, 63, 354-361. (in Japanese)

Kocaba, V., (2009), “Development and evaluation of methods to follow microstructural development of cementitious systems including slags.” Thesis (PhD). École Polytechnique Fédérale de Lausanne.

Kurumisawa, K., Nawa, T. and Owada, H., (2012). “Prediction of the diffusivity of cement-based materials using a three-dimensional spatial distribution model.” Cement and Concrete Composites, 34(3), 408-418.

Lothenbach, B., Matschei, T., Möschner, G. and Glasser, F. P.,(2008). “Thermodynamic modelling of the effect of temperature on the hydration and porosity of portland cement.” Cement and Concrete Research, 38 (1), 1-18.

Lothenbach, B., Scrivener, K. and Hooton, R. D., (2011). “Supplementary cementitious materials.” Cement and Concrete Research, 41(12), 1244-1256.

Luan, Y., Ishida, T., Nawa, T. and Sagawa, T., (2012). “Enhanced Model and Simulation of Hydration Process of Blast Furnace Slag in Blended Cement.” Journal of Advanced Concrete Technology, 10(1), 1-13.

Maekawa, K., Ishida, T. and Kishi, T., (2003). “Multi-scale modeling of concrete performance.” Journal of Advanced Concrete Technology, 1(2), 91-126.

Malhorta, V., (2000) “Durability of concrete.” In: R. W. Revie (Ed) Corrosion, Wiley.

Myers, R. J., Bernal, S. A. and Provis, J. L., (2014). “A


thermodynamic model for C-(N-)A-S-H Gel: CNASH_ss. Derivation and validation.” Cement and Concrete Research, 66, 27-47.

Nakarai, K., Ishida, T. and Maekawa, K., (2006). “Multi-phase physicochemical modeling of soil-cementitious material interaction.” Soils and Foundations, 46(5), 653-663.

Niwase, K., Naoyuki, S. and Tsuji, Y., (2010). “Materials and proportion’s design of self-compacting mortar used for low diffusion layer in sub-surface radioactive waste disposal facility in Japan.” Cement Research and Technology, 3, 43-51. (in Japanese)

Parkhust, D. L. and Appelo, C. A. J., (1999). “A computer program for speciation, batch-reaction, one- dimensional transport and inverse geochemical calculations.” USGS report.

Patel, R. A., Phung, O. T., Seetharam, S. C., Perko, J., Jacques, D., Naes, N., De Schutter, G., Ye, G. and van Breugel, K., (2016). “Diffusivity of saturated ordinary portland cement-based materials: A critical review of experimental and analytical modelling approaches.” Cement and Concrete Research, 90, 52-72.

Promentilla, M. A. B., Sugiyama, T., Hitomi, T. and Takeda, N., (2009). “Quantification of tortuosity in hardened cement pastes using synchrotron-based X-Ray computed microtomography.” Cement and Concrete Research, 39(6), 548-557.

Saeki, T. and Sasaki, K., (2006). “Chloride binding

capacity of calcium silicate hydrate.” Cement Science and Concrete Technology, 60, 322-327. (in Japanese)

Samson, E. and Marchand, J., (2007). Modelling the transport of ions in unsaturated cement-based materials.” Computer & Structures, 85, 1740-1756

Snyder, K. A., Feng, X., Keen, B. D. and Mason, T. O., (2003). “Estimating the electrical conductivity of cement paste pore solutions from OH-, K+ and Na+ concentrations.” Cement and Concrete Research, 33(6), 793-798.

Taylor, R., Richardson, I. G. and Brydson, R. M. D., (2010). “Composition and microstructure of 20-year-old ordinary portland cement-ground granulated blast-furnace slag blends containing 0 to 100% slag.” Cement and Concrete Research, 40(7), 971-983.

Tennis, P. D. and Jennings, H. M., (2000). “Model for two types of calcium silicate hydrate in the microstructure of portland cement pastes.” Cement and Concrete Research, 30(6), 855-863.

Torquato, S., (2001). “Random heterogeneous materials: Microstructure and macroscopic properties.” Springer.

Yamaguchi, T., Negishi, K. and Hoshino, S., (2009). “Modeling of diffusive mass transport in micropores in cement based materials.” Cement and Concrete Research, 39(12), 1149-1155.

Yu, S. W. and Page C. L., (1991). “Diffusion in cementitious materials: 1. Comparative study of chloride and oxygen diffusion in hydrated cement pastes.” Cement and Concrete Research, 21(4), 581-588.

Documents

The Impact of Tortuosity on Chloride Ion Diffusion in Slag ......The Impact of Tortuosity on Chloride Ion Diffusion in Slag-Blended Cementitious Materials AkiraHatanaka,Yogarajah Elakneswaran